| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 200.1-a4 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.16409$ |
$(a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.406960782$ |
1.272179997 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -107 a - 185\) , \( -892 a - 1545\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-107a-185\right){x}-892a-1545$ |
| 200.1-b4 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.16409$ |
$(a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.683761292$ |
$32.60784567$ |
1.609073952 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -108 a - 187\) , \( 705 a + 1223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-108a-187\right){x}+705a+1223$ |
| 3600.1-c4 |
3600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.921018641$ |
1.997925987 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 80\) , \( -200 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-80\right){x}-200a-1$ |
| 3600.1-k4 |
3600.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.39775$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.921018641$ |
1.997925987 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -78\) , \( 120 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}-78{x}+120a$ |
| 5000.1-e4 |
5000.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
5000.1 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$2.60299$ |
$(a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.881392156$ |
2.035487995 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2674 a - 4681\) , \( 97503 a - 169051\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2674a-4681\right){x}+97503a-169051$ |
| 5000.1-f4 |
5000.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
5000.1 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$2.60299$ |
$(a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.933393502$ |
$6.521569135$ |
3.514440935 |
\( \frac{132304644}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2675 a - 4679\) , \( -102184 a + 177075\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2675a-4679\right){x}-102184a+177075$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
